The produced energies of the series-parallel, total-cross-tied and multi-string configura-tions when a shadow with six transition steps is moving perpendicular and parallel to the strings of the PV generator array are presented as a function of the length of array sides in Figures 7.35 and 7.36, respectively. It is good to remember that the relative mismatch losses of the SP and TCT configurations are almost negligible when a shadow is moving perpendicular to the strings of a PV generator array. Thus, although the MS configuration has no mismatch losses in that case, the difference between the produced energies of the MS configuration and the other configurations is very small. In the case of a shadow moving parallel to the strings of a PV generator array, the mismatch losses of all the configurations are equal. Thus, also the produced energies of all the configura-tions are equal. Consequently, the configuration of a PV generator has only a minor effect on the mismatch losses of the generator when a shadow is moving perpendicular to the strings of the array and no effect when a shadow is moving parallel to the strings of the array.
Figure 7.35. The produced energies of the series-parallel, total-cross-tied and multi-string configurations as a function of the length of array sides when a shadow with six
transition steps is moving perpendicular to the strings of the PV generator array.
Figure 7.36. The produced energies of the series-parallel, total-cross-tied and multi-string configurations as a function of the length of array sides when a shadow with six
transition steps is moving parallel to the strings of the PV generator array.
When a shadow is moving diagonal to the array of a PV generator, every con-figuration has different amount of mismatch losses. Thus, also the produced energies of configurations differ from each other. The produced energies of the series-parallel, to-tal-cross-tied and multi-string configurations when a shadow with six transition steps is moving diagonal to the array of the PV generator array are presented as a function of the length of array sides in Figure 7.37. At the large sizes of the generator array, the energy produced by the MS configuration is substantially higher than the energy produced by
the SP or TCT configurations. The difference between the energies produced by the SP and TCT configurations is quite small.
Figure 7.37. The produced energies of the series-parallel, total-cross-tied and multi-string configurations as a function of the length of array sides when a shadow with six
transition steps is moving diagonal to the PV generator array.
When comparing the energies produced by different configurations, it is good to remember that the duration of the simulation period is dependent on the movement di-rection of a shadow. The duration of the simulation period is longest when a shadow is moving diagonal to the array of a PV generator and shortest when it is moving perpen-dicular to the strings of the array.
The simulations showed that the shadow sensitivity of the MS configuration is lower than the one of the SP and TCT configurations. When a shadow is moving paral-lel to the strings of the PV generator array, no reduction of mismatch losses is achieved by using the MS configuration. In addition, the achieved reduction is almost negligible when a shadow is moving perpendicular to the strings of the array. However, the achieved reduction is significant when a shadow is moving diagonal to the array. When the movement direction of a shadow is something between perpendicular and parallel to the strings of the array, some reduction of mismatch losses is achieved by using the MS configuration.
The MS configuration has some drawbacks owing to DC-DC converters, which need to be taken into account when evaluating the profitability of this configuration.
First of all, DC-DC converters raise the purchase and maintenance costs of the PV gen-erator, and secondly they decrease the efficiency and the reliability of the generator.
In several studies [11, 13, 14] have been found that the TCT configuration re-duces mismatch losses resulting from partial shading compared to the SP configuration.
The simulations showed that the shadow sensitivity of the SP configuration differs from the one of the TCT configuration only in the case of a cloud moving diagonal to the array of a PV generator. At the small sizes of the array, the shadow sensitivity of the
transition of the irradiance on the edge of a shadow is assumed to be linear, the tempera-ture of modules is assumed to be constant during the simulation period, temperatempera-ture and irradiance are assumed to be constant in the whole area of a PV module and all modules in a PV generator are assumed to be identical. The simulation model has been fitted to the characteristic of the NAPS NP190GKg PV module. The results of the simulations could slightly change if different PV modules were used. However, the basic behaviour would not change because it is the same for all Si PV modules.
Due to the cross-connections of the TCT configuration, the resistive losses in cables would increase the losses of the TCT configuration more than the ones of the SP and MS configurations. If resistive losses were taken into account, the losses of the TCT configuration compared to the ones of the SP configuration would not change in the cases of clouds moving parallel or perpendicular to the string of an array because there are no currents in the cross-connection of the TCT configuration. In the case of a cloud moving diagonal to the array, there are currents in the cross-connection of the TCT con-figuration. Thus, in that case, the losses of the TCT configuration would increase com-pared to the ones of the SP configuration if resistive losses in cables were taken into account.
Naturally, the achieved reduction of mismatch losses depends on the cloudiness of the location of a PV generator. In areas where cloudiness is low, mismatch losses are smaller than in areas where cloudiness is abundant. If the district where a PV generator is planned to be built has the dominant direction of clouds, the generator should be lo-cated so that this direction is perpendicular to the strings of the generator array. Based on the simulations, the shadow sensitivity of the MS configuration is lower than the one of the SP and TCT configurations. However, during equal conditions, the efficiency of the MS configuration is somewhat lower than the one of the SP and TCT configurations due to DC-DC converters. During equal conditions, the efficiency of the SP configura-tion matches up with the one of the TCT configuraconfigura-tion, because there is no current flow-ing through the cross-connections of the TCT configuration. Consequently, the size of the PV generator array and the cloudiness of the district where the generator is planned to be built determine which configuration is the most functional.
8 CONCLUSIONS
PV generators are composed of series- and parallel-connected PV modules. In grid-connected applications, PV modules are grid-connected in series in order to increase the voltage level for interfacing equipment used for connecting PV generators to the utility grid. Partial shading has many harmful effects on the operation of PV generators and a series connection is more prone to these effects than a parallel connection. Partial shad-ing can be due to, inter alia, passshad-ing clouds, surroundshad-ing buildshad-ings or trees, soilshad-ing or dirt accumulation on module frames. One of the major effects of partial shading is the occurrence of mismatch losses, which are the difference between the sum of the maxi-mum power outputs of individual modules and the output of the system. In practice, some mismatch losses occur always. Thus, the effective power of a PV generator is al-ways lower than the rated power of the generator.
The aim of this thesis was to study the shadow sensitivity of different configura-tions of a PV generator. This was studied by simulaconfigura-tions using the experimentally veri-fied MATLAB Simulink model of a PV generator and parameters for the NAPS NP190GKg PV module. The studied configurations were series-parallel, total-cross-tied and multi-string. All the studied configurations had an array in the shape of a square and were connected to the utility grid by one centralized inverter. The length of array sides was varied from 1 module up to 60 modules. The shadow sensitivity of configurations was studied with three movement directions of shadows: perpendicular to the strings of a PV generator array, parallel to the strings of the array and diagonal to the array. In addition, the sharpness of a shadow was varied.
The simulations showed that the mismatch losses of a PV generator are smallest when a shadow is moving perpendicular to the strings of the generator array. In that case, the MS configuration has no mismatch losses and the mismatch losses of the SP and TCT configurations are equal. However, the mismatch losses of the SP and TCT configurations are almost negligible. Thus, the configuration of a PV generator has only a minor effect on the mismatch losses of the generator when a shadow is moving per-pendicular to the strings of the generator array. When a shadow is moving parallel to the strings of a PV generator array, every configuration has equal mismatch losses. Thus, the configuration of a PV generator has no effect on the mismatch losses of the genera-tor when a shadow is moving parallel to the strings of the generagenera-tor array. When a shadow is moving diagonal to a PV generator array, every configuration has different amount of mismatch losses. At very small array sizes, the TCT configuration has the lowest mismatch losses. When the array size increases, the mismatch losses of the TCT configuration exceed first the ones of the MS configuration and then the ones of the SP
tion only in the case of a cloud moving diagonal to the array of a generator. However, the difference between these two configurations is small in that case.
The difference between the produced energies of different PV generator configu-rations depends on the cloudiness of the location of the generator. In order to select the optimal configuration of a PV generator, the cloudiness and the dominant direction of clouds of the location, where the generator is planned to be built, must be evaluated.
Based on the simulations, a PV generator should be located so that the dominant direc-tion of clouds is perpendicular to the strings of the generator array. The shadow sensi-tivity of the MS configuration is lower than the one of the SP and TCT configurations.
However, during equal operating conditions, the efficiency of the MS configuration is somewhat lower than the one of the SP and TCT configurations due to DC-DC convert-ers. In addition, DC-DC converters raise the purchase and maintenance costs and de-crease the reliability of a generator. Consequently, the size of the PV generator array and the cloudiness of the district where the generator is planned to be built determine which configuration is the most functional.
The simulation model used in simulations included some simplifications and it was fitted to the characteristic of the NAPS NP190GKg PV module. The results of the simulations could have slightly changed if a more accurate model or different PV mod-ules had been used. However, the basic behaviour would not change. Thus, the simula-tion model was accurate enough to the purposes of this thesis. The accuracy of the simu-lation model could be improved by taking the resistive losses in cables into account. In addition, single PV cells can be modelled individually, in which case changing condi-tions can be modelled more accurately. In order to study further the effects of moving clouds on the operation of PV generators, the effect of clouds on irradiance must be studied further. The shading model used in simulations included some simplifications and only three moving directions of shadows. The effects of different kinds of clouds on the operation of PV generators should be studied. In addition, the effects of other shad-ing sources should be studied. Only three different configurations were studied in this thesis. In order to study the effect of the configuration of a PV generator on the opera-tion of the generator, also other configuraopera-tions must be studied. In addiopera-tion, the optimal amount of strings connected in one DC-DC converter and the effect of the amount of cross-connections of an array on the mismatch losses of the generator should be studied.
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